Temporally unstructured quantum computation

Shepherd, Dan; Bremner, Michael J.

doi:10.1098/rspa.2008.0443

Cited by 159 publications

(307 citation statements)

References 21 publications

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“…Accordingly, Λ(Λ(Z)) can be performed on three qubits included in the first n qubits by using 25 white qubits and 105 black qubits as the ancillary qubits. From the above, at most m ancillary qubits are needed to construct C (2) f . However, in general, some of m ancillary qubits are not used.…”

Section: Lemma 2 For Any Degree-3 Polynomialmentioning

confidence: 99%

“…For any y ∈ {0, 1} n , let p y = Pr[C (2) f,0 n outputs y0 m ] and q y = Pr[A outputs y0 m on input C (2) f,0 n ]. From Stockmeyer's counting theorem, there is an FBPP NP algorithm that producesq y such that |q y − q y | ≤ q y /poly(n).…”

Section: Theorem 5 If the Output Probability Distribution Of Any Adiqmentioning

confidence: 99%

“…f,x (x ∈ {0, 1} n ) be the circuit produced by applying HZH to C (2) f for each kth white qubit such that…”

Section: Theorem 5 If the Output Probability Distribution Of Any Adiqmentioning

confidence: 99%

“…[6], in the argument to prove theorem 6, the initial state of each of the ancillary qubits is set to |0 to construct C (2) f . In other words, if we construct C (2) f without setting the initial state of each of them to |0 when f is chosen uniformly at random, we can prove theorem 6 for ǫ =const. The initial state of each of the ancillary qubits that are used to perform Λ(Z) does not have to be set to |0 to construct C (2) f .…”

Section: Theorem 5 If the Output Probability Distribution Of Any Adiqmentioning

confidence: 99%

“…Recently, in order to develop an understanding of the difference between them, the classical simulatability of restricted quantum computation has been extensively studied. For such quantum computation, commuting quantum computation including instantaneous quantum polynomial time (IQP) [2][3][4][5][6][7], deterministic quantum computation with 1 pure qubit (DQC1) [8][9][10], boson sampling [11][12][13][14], constant-depth quantum circuit [15,16], and permutational quantum computing [17] have been proposed.…”

Section: Introductionmentioning

confidence: 99%

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Ancilla-driven instantaneous quantum polynomial time circuit for quantum supremacy

Takeuchi

Takahashi²

2016

Phys. Rev. A

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Instantaneous quantum polynomial time (IQP) is a model of (probably) non-universal quantum computation. Since it has been proven that IQP circuits are unlikely to be simulated classically up to a multiplicative error and an error in the l1 norm, IQP is considered as one of the promising classes that demonstrates quantum supremacy. Although IQP circuits can be realized more easily than a universal quantum computer, demonstrating quantum supremacy is still difficult. It is therefore desired to find subclasses of IQP that are easy to implement. In this paper, by imposing some restrictions on IQP, we propose ancilla-driven IQP (ADIQP) as the subclass of commuting quantum computation suitable for many experimental settings. We show that even though ADIQP circuits are strictly weaker than IQP circuits in a sense, they are also hard to simulate classically up to a multiplicative error and an error in the l1 norm. Moreover, the properties of ADIQP make it easy to investigate the verifiability of ADIQP circuits and the difficulties in realizing ADIQP circuits.

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Section: Lemma 2 For Any Degree-3 Polynomialmentioning

confidence: 99%

Section: Theorem 5 If the Output Probability Distribution Of Any Adiqmentioning

confidence: 99%

“…f,x (x ∈ {0, 1} n ) be the circuit produced by applying HZH to C (2) f for each kth white qubit such that…”

Section: Theorem 5 If the Output Probability Distribution Of Any Adiqmentioning

confidence: 99%

Section: Theorem 5 If the Output Probability Distribution Of Any Adiqmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Ancilla-driven instantaneous quantum polynomial time circuit for quantum supremacy

Takeuchi

Takahashi²

2016

Phys. Rev. A

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Quantum Computation using Arrays of N Polar Molecules in Pendular States

Cao

Kais

et al. 2016

ChemPhysChem

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We investigate several aspects of realizing quantum computation using entangled polar molecules in pendular states. Quantum algorithms typically start from a product state |00⋯0⟩ and we show that up to a negligible error, the ground states of polar molecule arrays can be considered as the unentangled qubit basis state |00⋯0⟩ . This state can be prepared by simply allowing the system to reach thermal equilibrium at low temperature (<1 mK). We also evaluate entanglement, characterized by concurrence of pendular state qubits in dipole arrays as governed by the external electric field, dipole-dipole coupling and number N of molecules in the array. In the parameter regime that we consider for quantum computing, we find that qubit entanglement is modest, typically no greater than 10 , confirming the negligible entanglement in the ground state. We discuss methods for realizing quantum computation in the gate model, measurement-based model, instantaneous quantum polynomial time circuits and the adiabatic model using polar molecules in pendular states.

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Noisy Random Quantum Circuit Sampling and its Classical Simulation

Zhang

Wang²,

Han

2023

Adv Quantum Tech

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Demonstrating quantum advantage on noisy quantum devices is one of the most important tasks of quantum computing research in the near future. Random quantum circuit sampling is proposed as the most promising approach to the task and has been implemented in experiments for achieving quantum advantage. A series of encouraging computational complexity results, based on some plausible assumptions, show that this task is impossible to complete efficiently by classical computers. However, in practical experiments on noisy quantum devices, the approximate average‐case hardness and the effects of the noise need to be further checked. The competition between the classical simulation algorithm (mainly based on tensor network algorithms) and noisy quantum devices is the explicit way to understand quantum advantage in practice. This review briefly overviews the computational complexity arguments for the hardness of classical simulation of random quantum circuits sampling, then focus on various methods of classical simulation of quantum circuits based on tensor network method.

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Temporally unstructured quantum computation

Cited by 159 publications

References 21 publications

Ancilla-driven instantaneous quantum polynomial time circuit for quantum supremacy

Ancilla-driven instantaneous quantum polynomial time circuit for quantum supremacy

Quantum Computation using Arrays of N Polar Molecules in Pendular States

Noisy Random Quantum Circuit Sampling and its Classical Simulation

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